34 citations · 239 across the 41 of their papers we have counts for
6 papers · 1 filter
The fundamental theorem of finite fields: a proof from first principles
Anastasia Chavez, Christopher O'Neill
A mathematics student's first introduction to the fundamental theorem of finite fields (FTFF) often occurs in an advanced abstract algebra course and invokes the power of Galois th…
Numerical semigroups, polyhedra, and posets III: minimal presentations and face dimension
Tara Gomes, Christopher O'Neill, Eduardo Torres Davila
This paper is the third in a series of manuscripts that examine the combinatorics of the Kunz polyhedron , whose positive integer points are in bijection with numerical semigr…
On length densities
Scott T. Chapman, Christopher O'Neill, Vadim Ponomarenko
For a commutative cancellative monoid , we introduce the notion of the length density of both a nonunit , denoted , and the entire monoid , denoted $\…
On minimal presentations of shifted affine semigroups with few generators
Christopher O'Neill, Isabel White
An affine semigroup is a finitely generated subsemigroup of , and a numerical semigroup is an affine semigroup with . A growing body of recent work…
Factorization length distribution for affine semigroups III: modular equidistribution for numerical semigroups with arbitrarily many generators
Stephan Ramon Garcia, Mohamed Omar, Christopher O'Neill +1
For numerical semigroups with a specified list of (not necessarily minimal) generators, we describe the asymptotic distribution of factorization lengths with respect to an arbitrar…
Weighted Means of B-Splines, Positivity of Divided Differences, and Complete Homogeneous Symmetric Polynomials
Albrecht Boettcher, Stephan Ramon Garcia, Mohamed Omar +1
We employ the fact certain divided differences can be written as weighted means of B-splines and hence are positive. These divided differences include the complete homogeneous symm…